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On the basis of mechanism structure and the flash temperature theory, the instantaneous contact temperature-rise principle of constantly no clearance precision steel ball equal-speed transmission is studied and the formulas of the spin speed on each contact point, maximum contact stress, and frictional power are derived. Meantime, the mathematical model of instantaneous contact temperature risen of engagement pairs is established. By the use of MATLAB programming, the change curves of maximum contact stress of engagement pairs in one motion cycle are drawn, the rated loads with different design parameters are calculated, and the instantaneous contact temperature-rise of engagement pairs in one motion cycle are drawn. Besides, the effects on instantaneous contact temperature-rise caused by design parameters like groove angle and eccentricity are analyzed. It is shown that the maximum value of the instantaneous contact temperature-rise appears when the steel ball position angle is π and the inner side bears the pressure. The research findings lay a theoretical foundation for the scuffing load capacity calculation of the contact engagement pairs and thermo-mechanical analysis of constantly no clearance precision steel ball transmission.